THE 2002 ELECTIONS: THE SENATE -- Texas; Passing the Torch In Bush Country

John Cornyn, a Republican, declared victory tonight in his Senate race against his Democratic opponent, Ron Kirk, after a closely fought campaign in which President Bush made home-state appearances to bolster Mr. Cornyn.

Final returns had not been announced nor had Mr. Kirk conceded before Mr. Cornyn, the state's attorney general, appeared at 10:15 p.m. to claim victory before cheering supporters. He was introduced by the man he would succeed, Senator Phil Gramm, who is retiring, and by the other Republican senator from Texas, Kay Bailey Hutchison.

''I accept with great humility the honor of following Phil Gramm in the United States Senate,'' Mr. Cornyn said. ''Phil, they are awfully big shoes to fill.''

Mr. Cornyn promised to support Mr. Bush in approving federal judges and to help push through the administration's energy policy.

Mr. Cornyn enjoyed a solid lead with 53 percent of precincts reporting at 11 p.m. He had 56 percent of the vote compared with 43 for Mr. Kirk, who had refused to concede.

Other Democrats noted that the election might not be decided until Wednesday, as voting irregularities in San Antonio and Fort Worth might mean delays in the final tallies.

If Mr. Cornyn maintains his lead, the victory would be an enormous relief for the Republican Party and Mr. Bush. The election attracted intense attention from both national parties, as Democrats saw a ripe opportunity to embarrass Mr. Bush and make history if Mr. Kirk became the first black senator from the state. Republicans were determined to hold the seat.

Unlike the campaign for governor here, the nastiest in recent memory, the Senate race has been a mostly gentlemanly affair. Both candidates largely pushed the issue of race aside. Mr. Cornyn left little doubt that a centerpiece of his campaign was his unstinting support of Mr. Bush, while portraying Mr. Kirk as opposed to the president's agenda.

Mr. Bush appeared at a rally for Mr. Cornyn on Monday night in Dallas, and campaign advertising for Mr. Cornyn showed the two together. Mr. Cornyn has also been helped by Laura Bush and Karen P. Hughes, Mr. Bush's longtime adviser. Mr. Bush has appeared at fund-raisers for Mr. Cornyn.

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''What Cornyn did was say, 'I stand foursquare with George W. Bush,' '' said Calvin Jillson, a professor of political science at Southern Methodist University in Dallas.

Mr. Kirk, who resigned as mayor of Dallas to run, positioned himself as a centrist who would work toward bipartisan solutions in Washington. He cited his record of building coalitions in Dallas and often voiced support for Mr. Bush, who is hugely popular in Texas.

''Kirk sort of represents the next wave of black political leadership in the South,'' Mr. Jillson said. ''He ran a moderate, business-friendly campaign.''

The final results could be delayed until Wednesday, after election officials in Tarrant County, which includes Fort Worth and is the fourth-most-populous county in the state, said that problems with voting machines would require a recount of all ballots. County officials found that all ballots in which voters punched a straight party ticket had gone uncounted.

The recount began tonight after the polls closed. The recount, officials said, could involve up to 360,000 votes.

Experts watched the race for clues to changes in voting trends. Mr. Kirk was part of what some Democrats called a dream team intended to tap into the state's ethnically diverse population. Party leaders hoped that the candidate for governor, Tony Sanchez, would attract Hispanic voters, that Mr. Kirk would attract black ones and that the centrist tone of the slate would help the party regain white voters lost to Republicans in recent elections.

The Democrats faced long odds. Republicans have dominated state elections for a decade and hold every statewide elected office. Although Mr. Bush is not on the ballot, Republicans eagerly attached themselves to his popularity.

Mr. Cornyn and Mr. Kirk spent the final days of the campaign imploring core supporters to turn out on Election Day. Mr. Cornyn appeared at a high school football game in Abilene and then went to church services in San Antonio before his appearance with Mr. Bush on Monday night in Dallas.

Mr. Kirk, suffering from a nasty cold, canceled a Friday night appearance at a football game but recovered in time to attend church services in Houston. He also held a final weekend fund-raiser in Houston that featured a performance by Stevie Wonder. JIM YARDLEY